=== Base Templates !SpecializationAsEnd1UniversalRestriction, !SpecializationAsEnd2UniversalRestriction ===
[[br]]!SpecializationAsEnd1UniversalRestriction and !SpecializationAsEnd2UniversalRestriction
are templates for expressing relation specialisations with the force of universal restriction.
These templates have the same roles, and similar definitions except for the use of reference
items !End1UniversalRestriction, resp. !End2UniversalRestriction.
[[br]]
[[br]]!SpecializationAsEnd1UniversalRestriction means that a and b are relations, that a is a
subrelation of b, and that the specialization relation between a and b is a member of
End1UniversalRestriction.
[[br]]
[[br]]Roles:
[[br]]1 hasSubrelation !ClassOfRelationship
[[br]]2 hasSuperrelation !ClassOfRelationship
Axiom:
{{{
SpecializationAsEnd1UniversalRestriction(x1, x2) <->
ClassOfRelationship(x1) &
ClassOfRelationship(x2) &
exists y(SpecializationTriple(y, x1, x2)&
ClassificationTemplate(y, End1UniversalRestriction))
}}}
Axiom:
{{{
SpecializationAsEnd2UniversalRestriction(x1, x2) <->
ClassOfRelationship(x1) &
ClassOfRelationship(x2) &
exists y(SpecializationTriple(y, x1, x2)&
ClassificationTemplate(y, End2UniversalRestriction)) .
}}}
NOTE A statement !SpecializationAsEnd1UniversalRestriction(a, b) implies that the specialization
of b to a has the force of a universal restriction on the class that is the domain of a: any pair in b for which the first element is a member of the domain of a is a member of a. (Accordingly, !SpecializationAsEnd2UniversalRestriction(a, b) constrains the range of a). See 8.4 for further information on the representation used in this template.